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Suppose that the expected return and standard deviation of stock A are 10% and 5% respectively,...

Suppose that the expected return and standard deviation of stock A are 10% and 5% respectively, while the expected return and standard deviation of stock B are 15% and 10% respectively. Returns of stock A and B are perfectly negatively correlated. Also suppose that it is possible to borrow at the risk-free rate. What must be the value of the risk-free rate?

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Answer #1

We can calculate the risk free rate by creating risk free portfolio with stock A and Stock B.

Provided,

rA = 10%

= 5%

rB = 15%

= 10%

= -1

where,

rA = Expected return of A

= Standard deviation of A

rB = Expected return of B

= Standard deviation of B

= Correlation between A and B

Composition of Risk Free Portfolio:

where,

Weight of stock A in Risk free asset

and

wB = (1-wA)

Putting the value to compute the weight

and

Thus, Risk free rate would be:

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